Continuing the recent debate surrounding Peter Hallward’s critique of Quentin Meillassoux’s After Finitude, Larval Subjects points towards the principal issue at hand: the questionable legitimacy of ontological systems predicated on the primacy of the matheme and the supposed “purity” of mathematical discourse as the 'royal road' to an uncontaminated being. The real target here is of course Alain Badiou’s identification of the discourse of being (ie- ontology) with axiomatic set theory. However Badiou (unlike his pupil) is careful to maintain a distinction between ontology as discourse (that which can be said of being) and being itself. Set theory then enables a kind of purified discourse about being, without ever necessarily entailing access to being itself. This “purification” is the removal from ontological discourse of the ontic dimension, of all predicates and qualities that might be applied to something, to leave behind merely the most minimal descriptions of a being (that to say something “is” is the least that can be said in a process of reduction whilst still allowing it to “be”). As Badiou describes: “Strictly speaking mathematics presents nothing […] because not having anything to present, besides presentation itself – which is to say the multiple – and thereby never adopting the form of the ob-ject, such is a condition of all discourse on being qua being.” It is important to realise that this mathematised ontology does not mean that, for example, actual beings are ultimately composed of infinite multiplicities of number! As Badiou himself puts it: “The thesis that I support does not in any way declare that being is mathematical, which is to say composed of mathematical objectivities. It is not a thesis about the world but about discourse. It affirms that mathematics, throughout the entirety of its historical becoming, pronounces what is expressible of being qua being.” The reason for this is discernible in Badiou’s decision of the multiple over the one, since “what presents itself is essentially multiple; what presents itself is essentially one”- and hence to describe presentation outside of the “what” dimension (i.e.- the ontic) is a necessary step to holding the one at bay, a step achieved by handing over the business of ontology to set theory. As Larval Subjects correctly analyses, mathematics does not give us “all that can be said of being”, and it is not part of Badiou’s project (within Being and Event at least) to even attempt to do so… instead mathematics is positioned as the least which can be said of being, a modest minimalism…
There appear to be three issues here:
(1) That mathematical ontologies allow for the description of entities which do not exist in the corporeal world (ie- the problem of non-Euclidean geometry). For Meillassoux (as Hallward accurately diagnoses) this means that deductions vouchsafed within a realm of pure maths cannot legitimately be automatically shifted into the real world (ie- that of applied mathematics). This is certainly an issue for Meillassoux, but how serious is this for Badiou?
(2) That in terms of a broader notion of “being” mathematised ontologies such as Badiou’s set theoretical notion do not give an exhaustive description of every aspect of being. This is undoubtedly correct, but Badiou would not want to deny this, his interpretation of “being” being oriented towards a minimalistic definition of the least which one can say before being unable to describe any being at all. Set theoretical descriptions of situations are preferred by Badiou precisely because they enable the indiscriminate counting of things without any necessary ontical detailing of what the thing is, and hence an apparently universal discourse, (which can as easily describe humans in a class room as grains of sand on a beach etc). Hence being-qua-being is already a particular sub-genre or specific sense of being.
(3) That the claim towards a “materialism” appears to be restricted to the “matter” of number itself, (or as Meillassoux has stated “the meaningless symbols of mathematics”). If this “matter” produces forms which are only possible within thought and which fails (whether by design or not) to describe every aspect of being, indeed, to describe an aspect of being which is reducible from the ontic dimensions only in thought itself, how does this not collapse into a cunningly scientistic idealism?
In sum then: Given (1) mathematised ontologies invariably enable the description of entities which do not exist outside the mind and (2) denote a “pure” being, a kind of being which has no existence outside of the mind capable of conceptualising being divorced of its ontic dimensions then (3) this materialism seems to be simply an idealism. Or at least, as guarded against by Badiou’s discursive shield, an idealist discourse. Meillassoux seems to move beyond this protective layer towards a notion of mathematical information (as indexed by ancestral phenomena such as the archefossil) being present within phenomena themselves… If anything Hallward does not make a strong enough case here, given that it is to retain a correlation (to a mathematising consciousness) to ascribe to things-in-themselves any mathematical properties (i.e.- beyond Hallward’s argument as to dates requiring linguistic mediation contained in phrases like “6 billion years before the emergence of life”), perhaps… Is mathematics really in a superior position to language, (in its precision perhaps, as indicated by its ability to index primary qualities rather than merely secondary qualities) but does it really hold that it is truly a mind-independent property? If we are to pay close attention to Badiou’s sneaky but necessary discursive get-out-clause, then we might consider even a primary mathematisable quality within a thing to be merely a discursive representation of an irreducible and indifferent ontic being. Is it to travel too far into the correlationists' circle to contend even that mathematically indexable primary qualities are really present as anything other than an idealist discursive abstraction of the unreachable in-itself? Does mathematics really enable us, as Meillassoux contends, to access the "great outdoors" of thought (the thing-in-itself outside correlation, the pure object sundered from a subjective mediation)...? In a counterfactual situation where conscious life never emerges in the universe at all, (i.e.- a universe where correlation itself is impossible because of the inexistence of subjects) is it possible to think a mathematical property as being present within a given thing within this universe? If mathematics is simply a superior discourse, but a discourse none the less, how can we even ascribe primary qualities to objects in a universe devoid of conscious mediation? Is the real outside thought not the universe without even mathematical discourse? Or is mathematical discourse in the ontic sense merely a communicative way of expressing intrinsic relations between things which exist independently of any subjective mediation… is this the principle article of faith for a realist position, (the realist "kool aid" so to speak) to "buy into" the ability of mathematical information to be mind-independent? Is this the final correlationist trap or the pathway to the real outside?
There appear to be three issues here:
(1) That mathematical ontologies allow for the description of entities which do not exist in the corporeal world (ie- the problem of non-Euclidean geometry). For Meillassoux (as Hallward accurately diagnoses) this means that deductions vouchsafed within a realm of pure maths cannot legitimately be automatically shifted into the real world (ie- that of applied mathematics). This is certainly an issue for Meillassoux, but how serious is this for Badiou?
(2) That in terms of a broader notion of “being” mathematised ontologies such as Badiou’s set theoretical notion do not give an exhaustive description of every aspect of being. This is undoubtedly correct, but Badiou would not want to deny this, his interpretation of “being” being oriented towards a minimalistic definition of the least which one can say before being unable to describe any being at all. Set theoretical descriptions of situations are preferred by Badiou precisely because they enable the indiscriminate counting of things without any necessary ontical detailing of what the thing is, and hence an apparently universal discourse, (which can as easily describe humans in a class room as grains of sand on a beach etc). Hence being-qua-being is already a particular sub-genre or specific sense of being.
(3) That the claim towards a “materialism” appears to be restricted to the “matter” of number itself, (or as Meillassoux has stated “the meaningless symbols of mathematics”). If this “matter” produces forms which are only possible within thought and which fails (whether by design or not) to describe every aspect of being, indeed, to describe an aspect of being which is reducible from the ontic dimensions only in thought itself, how does this not collapse into a cunningly scientistic idealism?
In sum then: Given (1) mathematised ontologies invariably enable the description of entities which do not exist outside the mind and (2) denote a “pure” being, a kind of being which has no existence outside of the mind capable of conceptualising being divorced of its ontic dimensions then (3) this materialism seems to be simply an idealism. Or at least, as guarded against by Badiou’s discursive shield, an idealist discourse. Meillassoux seems to move beyond this protective layer towards a notion of mathematical information (as indexed by ancestral phenomena such as the archefossil) being present within phenomena themselves… If anything Hallward does not make a strong enough case here, given that it is to retain a correlation (to a mathematising consciousness) to ascribe to things-in-themselves any mathematical properties (i.e.- beyond Hallward’s argument as to dates requiring linguistic mediation contained in phrases like “6 billion years before the emergence of life”), perhaps… Is mathematics really in a superior position to language, (in its precision perhaps, as indicated by its ability to index primary qualities rather than merely secondary qualities) but does it really hold that it is truly a mind-independent property? If we are to pay close attention to Badiou’s sneaky but necessary discursive get-out-clause, then we might consider even a primary mathematisable quality within a thing to be merely a discursive representation of an irreducible and indifferent ontic being. Is it to travel too far into the correlationists' circle to contend even that mathematically indexable primary qualities are really present as anything other than an idealist discursive abstraction of the unreachable in-itself? Does mathematics really enable us, as Meillassoux contends, to access the "great outdoors" of thought (the thing-in-itself outside correlation, the pure object sundered from a subjective mediation)...? In a counterfactual situation where conscious life never emerges in the universe at all, (i.e.- a universe where correlation itself is impossible because of the inexistence of subjects) is it possible to think a mathematical property as being present within a given thing within this universe? If mathematics is simply a superior discourse, but a discourse none the less, how can we even ascribe primary qualities to objects in a universe devoid of conscious mediation? Is the real outside thought not the universe without even mathematical discourse? Or is mathematical discourse in the ontic sense merely a communicative way of expressing intrinsic relations between things which exist independently of any subjective mediation… is this the principle article of faith for a realist position, (the realist "kool aid" so to speak) to "buy into" the ability of mathematical information to be mind-independent? Is this the final correlationist trap or the pathway to the real outside?
